So I was just looking at some of the feathers that my ringneck has lost - she's currently moulting - and I noticed a mite/little bug.

I don't know how well you can see, but it was about 2mm long and had obviously been chewing holes in the feathers. I immediately checked my birds over but none of them have bald patches, holes in their feathers and they're all acting bright and alert as usual. Aside from looking scruffy due to the moult I can't see anything different about my ringneck.

Is this something I need to worry about or is this just something than happens to discarded feathers?

You need to get some 0.1% Ivermectin. I do mine once every 6 months as a preventative treatment because mites are absolutely horrible. I believe Rob Harvey does it if you go on their website. I got my last lot from there

Make sure you get 0.1% and not 1.0%. Clean everything very thoroughly and make sure that everybody gets a drop of that on the back of their necks (move the feathers out of the way to get to the bare skin)

If this is feather mite! I say this as there are a few types of mite.
And I can only say that I have seen a case of feather mites.
I guess you have looked along the shaft of the feathers. That is where you maybe able to see little bumps. Hold the wings up to a strong light.
If you see one the chances are there are more, I would be treating for them.